Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main() {
    int n;
    cin >> n;
    int a[n];
    for(int i=0;i<n;i++){
        cin >> a[i];
    }
    sort(a,a+n);

    long long int mindiv=5000000000000,mitr,lastmin;

    for(int i=0;i<n-3;i++){
        if(mindiv > (a[i+1]-a[i])){
            mindiv = a[i+1] - a[i];
            mitr = i;
        }
    }

    lastmin = a[n-1] - a[n-2];

    double ans = ((double)(a[n-1]+a[n-2])/(double)mindiv);
    if(mitr != n-3 && mitr !=n-4) {
        ans = max((double) (a[n - 3] + a[n - 4]) / (double) min(mindiv, lastmin),ans);
    }
    if(mitr != n-4 && mitr != n-5) {
        ans = max((double) (a[n - 1] + a[n - 4]) / (double)mindiv, ans);
    }

    cout << fixed << setprecision(10) << ans << endl;

    return 0;
}